Nothing. People are never going to stop being self-entitled armchair GMs and people are never going to stop pretending like they know what happens in the front office. Yeah the majority of the bandwagon will sway with the flavor of the month, so if the Jays make the playoffs and a few popular posters start rooting for AA again, you'll probably see several others chime in, in agreement, but even if the Jays win back-to-back world series, if they start struggling the season after, it'll be back to calling for AA's head.
Just look at the examples in front of you. Jays fans would have done anything for a 20-30M bump in payroll two years ago, today, 50M+ later, Rogers is still a bunch of swindling cheap villains. Red Sox fans were elated just six months ago about their star manager and their world series team, just a few months later, almost all of them are completely pissed with Farrell because they're realizing how garbage of a manager he always was. A month ago, we had a "Fire Seitzer" thread, today we've got one singing his praises. Hell, people even turn on the players themselves on a weekly or even nightly basis.
So the short answer is, the team can't do anything to change the way people are, no sports organization is perfect, and until that fact remains true, there will always be slip-ups and mistakes and missed opportunities, even by the best teams, and at every turn, there will be a group of "fans" ready to fiercely take their anger out on their poor keyboards.